Crash-Neutral Currency Carry Trades Jakub W. Jurek Princeton - PowerPoint PPT Presentation

Crash-Neutral Currency Carry Trades Jakub W. Jurek Princeton University – Bendheim Center for Finance March 2009

Currency Carry Trade Currency carry trades exploit violations of uncovered interest parity (UIP) by buying (selling) currencies with relatively high (low) interest rates.

Currency Carry Trade Historical returns: ◮ Before (USD/G10; monthly, 1990:1-2007:03) RMRF SMB HML UMD FX Carry Mean 0.0730 0.0227 0.0477 0.0985 0.0478 t-stat 2.13 0.75 1.72 2.51 3.91 St. dev. 0.1422 0.1261 0.1153 0.1630 0.0507 Skewness -0.68 0.81 0.11 -0.66 -0.95 SR 0.51 0.18 0.41 0.60 0.94

Currency Carry Trade Historical returns: ◮ Before (USD/G10; monthly, 1990:1-2007:03) RMRF SMB HML UMD FX Carry Mean 0.0730 0.0227 0.0477 0.0985 0.0478 t-stat 2.13 0.75 1.72 2.51 3.91 St. dev. 0.1422 0.1261 0.1153 0.1630 0.0507 Skewness -0.68 0.81 0.11 -0.66 -0.95 SR 0.51 0.18 0.41 0.60 0.94 ◮ After (USD/G10; monthly, 1990:1-2008:10) RMRF SMB HML UMD FX Carry Mean 0.0477 0.0191 0.0392 0.1060 0.0331 t-stat 1.39 0.68 1.50 2.83 2.55 St. dev. 0.1485 0.1223 0.1136 0.1628 0.0563 Skewness -0.84 0.83 0.11 -0.60 -1.63 SR 0.32 0.16 0.35 0.65 0.59

Paper Summary This paper tests the hypothesis that violations of UIP are attributable to crash risk premia by examining data on foreign exchange options: 1. Dynamics of risk-neutral skewness: ◮ Negatively related to contemporaneous interest rate differential in the cross-section; weak time-series relation. ◮ Does not forecast currency excess returns. ◮ Moves opposite to future realized skewness in response to realized currency moves.

Paper Summary This paper tests the hypothesis that violations of UIP are attributable to crash risk premia by examining data on foreign exchange options: 1. Dynamics of risk-neutral skewness: ◮ Negatively related to contemporaneous interest rate differential in the cross-section; weak time-series relation. ◮ Does not forecast currency excess returns. ◮ Moves opposite to future realized skewness in response to realized currency moves. 2. Crash-neutral currency carry trades: ◮ Returns smaller than for standard carry trades, but positive and statistically significant. ◮ Results robust to inclusion of transaction costs. ◮ Crash-based explanation would requires option implied volatilities that are 2-4x the actual values observed in the data.

Uncovered Interest Parity ◮ Uncovered interest parity (UIP) predicts that high interest currencies should depreciate relative to low interest rate currencies, such that investors are indifferent between holding deposits in the two. ◮ S t – spot exchange rate (price of foreign currency in USD) ◮ F t ,τ – forward exchange rate F t ,τ = S t · exp (( r d , t − r f , t ) · τ )

Uncovered Interest Parity ◮ Uncovered interest parity (UIP) predicts that high interest currencies should depreciate relative to low interest rate currencies, such that investors are indifferent between holding deposits in the two. ◮ S t – spot exchange rate (price of foreign currency in USD) ◮ F t ,τ – forward exchange rate F t ,τ = S t · exp (( r d , t − r f , t ) · τ ) ◮ Following Hansen and Hodrick (1989), UIP is typically tested by running a regression of the log currency return on the log forward spread: s t +1 − s t = a 0 + a 1 · ( f t − s t ) + ε t +1 = a 0 + a 1 · ( r d , t − r f , t ) · τ + ε t +1 ◮ Null hypothesis ( H 0 ): a 0 = 0 and a 1 = 1.

Uncovered Interest Parity Testing UIP in the panel of G10 currencies (Table I) The intercept of the UIP regression is negative for 6 of 9 countries in the full sample (1990-2007) and in all countries during the 1999-2007 sample. 1990-2007 1999-2007 R 2 χ 2 test R 2 χ 2 test Currency ˆ a 0 ˆ a 1 ˆ a 0 ˆ a 1 NFE NFE AUD -0.0025 -1.7483 0.0105 8.87 -0.0028 -3.9018 0.0310 9.34 (0.0023) (1.0522) (0.01) (0.0036) (1.9520) (0.01) CAD -0.0001 -0.5077 0.0019 9.13 0.0027 -2.5012 0.0115 5.06 (0.0009) (0.5104) (0.01) (0.0015) (2.1091) (0.08) CHF 0.0026 -1.2815 0.0069 5.60 0.0096 -4.5238 0.0350 9.03 (0.0024) (1.0008) (0.06) (0.0041) (1.8485) (0.01) EUR 0.0002 -0.0320 -0.0002 1.34 0.0036 -4.4836 0.0447 11.19 (0.0016) (0.9072) (0.51) (0.0024) (1.6590) (0.00) GBP 0.0021 0.7061 0.0020 3.65 0.0001 -1.7371 0.0061 4.55 (0.0019) (1.2755) (0.16) (0.0025) (1.7738) (0.10) JPY 0.0058 -2.0823 0.0165 12.33 0.0048 -1.8183 0.0099 6.20 (0.0025) (0.8787) (0.00) (0.0045) (1.4003) (0.05) NOK 0.0013 0.6255 0.0042 1.43 0.0007 -1.4005 0.0090 5.46 (0.0017) (0.6351) (0.49) (0.0026) (1.2175) (0.07) NZD -0.0047 -2.4128 0.0147 15.46 -0.0067 -4.7728 0.0482 17.15 (0.0034) (1.1975) (0.00) (0.0045) (1.6837) (0.00) SEK 0.0004 0.6081 0.0046 0.51 0.0026 -3.5247 0.0405 11.09 (0.0017) (0.6046) (0.77) (0.0024) (1.3764) (0.00) Pooled FE -0.1795 0.0002 2.59 FE -3.0503 0.0248 24.17 (0.6589) (0.99) (1.1190) (0.01) XS 0.0005 -0.1883 0.1070 - 0.0012 -0.5994 0.0966 - (0.0003) (0.0836) (0.0005) (0.1087) -

Uncovered Interest Parity Testing UIP in the panel of G10 currencies (Table I) At the 10% significance level, UIP is rejected in 5 of 9 countries in the full sample (1990-2007) and in all countries during the 1999-2007 sample. 1990-2007 1999-2007 R 2 χ 2 test R 2 χ 2 test Currency ˆ a 0 ˆ a 1 ˆ a 0 ˆ a 1 NFE NFE AUD -0.0025 -1.7483 0.0105 8.87 -0.0028 -3.9018 0.0310 9.34 (0.0023) (1.0522) (0.01) (0.0036) (1.9520) (0.01) CAD -0.0001 -0.5077 0.0019 9.13 0.0027 -2.5012 0.0115 5.06 (0.0009) (0.5104) (0.01) (0.0015) (2.1091) (0.08) CHF 0.0026 -1.2815 0.0069 5.60 0.0096 -4.5238 0.0350 9.03 (0.0024) (1.0008) (0.06) (0.0041) (1.8485) (0.01) EUR 0.0002 -0.0320 -0.0002 1.34 0.0036 -4.4836 0.0447 11.19 (0.0016) (0.9072) (0.51) (0.0024) (1.6590) (0.00) GBP 0.0021 0.7061 0.0020 3.65 0.0001 -1.7371 0.0061 4.55 (0.0019) (1.2755) (0.16) (0.0025) (1.7738) (0.10) JPY 0.0058 -2.0823 0.0165 12.33 0.0048 -1.8183 0.0099 6.20 (0.0025) (0.8787) (0.00) (0.0045) (1.4003) (0.05) NOK 0.0013 0.6255 0.0042 1.43 0.0007 -1.4005 0.0090 5.46 (0.0017) (0.6351) (0.49) (0.0026) (1.2175) (0.07) NZD -0.0047 -2.4128 0.0147 15.46 -0.0067 -4.7728 0.0482 17.15 (0.0034) (1.1975) (0.00) (0.0045) (1.6837) (0.00) SEK 0.0004 0.6081 0.0046 0.51 0.0026 -3.5247 0.0405 11.09 (0.0017) (0.6046) (0.77) (0.0024) (1.3764) (0.00) Pooled FE -0.1795 0.0002 2.59 FE -3.0503 0.0248 24.17 (0.6589) (0.99) (1.1190) (0.01) XS 0.0005 -0.1883 0.1070 - 0.0012 -0.5994 0.0966 - (0.0003) (0.0836) (0.0005) (0.1087) -

Currency Carry Trade The currency carry trade exploits deviations from UIP by borrowing funds in currencies with low interest rates and investing them in currencies with high interest rates. ◮ Investor constructs carry trades in X/USD currency pairs (X ∈ G10) ◮ Funds are borrowed/invested at the relevant one-month LIBOR rates. ◮ Positions are held for one month. ◮ Payoffs: � r f , t > r d , t : � � � � · ˜ exp r f , t · τ S t + τ − exp r d , t · τ · S t � � � � � CT t +1 = · ˜ r d , t > r f , t : exp r d , t · τ · S t − exp r f , t · τ S t + τ

Currency Carry Trade Portfolio strategies Consider the following portfolio formation rules: 1. Equal-weighted (EQL) 2. Spread-weighted (SPR) 3. Equal-weighted dollar-neutral (EQL-$N) 4. Spread-weighted dollar-neutral (SPR-$N) Portfolio USD Exposure Currency r f , t − r d , t EQL SPR AUD 1.88% -0.11 -0.14 CAD 0.05% -0.11 -0.00 GBP 1.28% -0.11 -0.09 NOK 1.29% -0.11 -0.09 NZD 2.78% -0.11 -0.20 CHF -2.11% 0.11 0.15 EUR -0.42% 0.11 0.03 JPY -3.45% 0.11 0.25 SEK -0.32% 0.11 0.02 Net USD - -0.11 -0.07

Currency Carry Trade Portfolio strategies Consider the following portfolio formation rules: 1. Equal-weighted (EQL) 2. Spread-weighted (SPR) 3. Equal-weighted dollar-neutral (EQL-$N) 4. Spread-weighted dollar-neutral (SPR-$N) Portfolio USD Exposure Currency r f , t − r d , t EQL SPR EQL-$N SPR-$N AUD 1.88% -0.11 -0.14 -0.20 -0.26 CAD 0.05% -0.11 -0.00 -0.20 -0.01 GBP 1.28% -0.11 -0.09 -0.20 -0.18 NOK 1.29% -0.11 -0.09 -0.20 -0.18 NZD 2.78% -0.11 -0.20 -0.20 -0.38 CHF -2.11% 0.11 0.15 0.25 0.33 EUR -0.42% 0.11 0.03 0.25 0.07 JPY -3.45% 0.11 0.25 0.25 0.55 SEK -0.32% 0.11 0.02 0.25 0.05 Net USD - -0.11 -0.07 0.00 0.00

Currency Carry Trade Historical performance (Figure 1) Simple portfolio construction rules (e.g. equal- and spread-weighting) were close to being ex post efficient.

Currency Carry Trade Historical performance – portfolio strategies (Table II) 1999:1-2007:3 (N = 99) EQL SPR EQL-$N SPR-$N Mean 0.0560 0.0844 0.0434 0.0699 t-stat 3.63 4.26 2.30 2.84 Std. dev. 0.0443 0.0569 0.0543 0.0707 Skewness -0.42 -0.20 -0.52 -0.23 Kurtosis 3.73 2.97 4.31 4.33 Min -0.0368 -0.0335 -0.0569 -0.0661 Max 0.0375 0.0455 0.0369 0.0651 Carry 0.0200 0.0307 0.0345 0.0478 SR 1.26 1.48 0.80 0.99